charity sells $6 raffle tickets first prizes to trace worth $3,000 2nd prize of $600 third prize is $40 and fourth prize $15 they sell 600 tickets what is the expected value
To calculate the expected value, we need to multiply the value of each prize by its corresponding probability and then sum them up.
Given:
- First Prize: $3,000
- Second Prize: $600
- Third Prize: $40
- Fourth Prize: $15
- Total number of tickets sold: 600
We also need to determine the probability of winning each prize. To do this, we divide the number of tickets sold for a particular prize by the total number of tickets sold.
- First Prize Probability: 1 / 600 (since only 1 first prize is available)
- Second Prize Probability: 1 / 600 (only 1 second prize available)
- Third Prize Probability: 1 / 600 (only 1 third prize available)
- Fourth Prize Probability: 1 / 600 (only 1 fourth prize available)
Now, we can calculate the expected value using the formula:
Expected Value = (First Prize Value x First Prize Probability)
+ (Second Prize Value x Second Prize Probability)
+ (Third Prize Value x Third Prize Probability)
+ (Fourth Prize Value x Fourth Prize Probability)
Expected Value = ($3,000 x 1/600) + ($600 x 1/600) + ($40 x 1/600) + ($15 x 1/600)
Simplifying this equation:
Expected Value = $3,000/600 + $600/600 + $40/600 + $15/600
= $5 + $1 + $0.067 + $0.025
= $6.092
Therefore, the expected value of a raffle ticket for this charity event is approximately $6.09.